We left Ireland 10 years ago - and didn't even think of closing down ALL out accounts - why do that???
We too rented out our house in Ireland, and there has been no problems with using our current bank account in Ireland, as well as other accounts.
We did close one or two accounts that we didn't need any longer, but we should have done that anyway, even if we didn't move abroad.
The only problem we have is that banks tend to reduce interest rates on accounts to something dismal after a while and, if you are a non-resident, it is hard to open a NEW account in Ireland (as well as in Britain).